Fig. 1

Comparison of Euclidean distance and (regularized) optimal transport losses. Synthetic musical notes are generated by putting weight on a fundamental, and exponentially decreasing weights on its harmonics and sub-harmonics, and finally convoluting with a Gaussian. Left: examples of the spectrograms of two such notes. Right: (regularized) optimal transport loss and Euclidean distance from the note of fundamental 0.95 kHz (red line on the left plot) to the note of fundamental 0.95 kHz + σ, as functions of σ. The Euclidean distance varies sharply whereas the optimal transport loss captures more smoothly the change in the fundamental. The variations of the optimal transport loss and its regularized version are similar, although the regularized one can become negative